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September 2013 Killing the $GCH$ everywhere with a single real
Sy-David Friedman, Mohammad Golshani
J. Symbolic Logic 78(3): 803-823 (September 2013). DOI: 10.2178/jsl.7803060

Abstract

Shelah—Woodin [10] investigate the possibility of violating instances of GCH through the addition of a single real. In particular they show that it is possible to obtain a failure of CH by adding a single real to a model of GCH, preserving cofinalities. In this article we strengthen their result by showing that it is possible to violate GCH at all infinite cardinals by adding a single real to a model of GCH. Our assumption is the existence of an $H(\kappa^{+3})$-strong cardinal; by work of Gitik and Mitchell [6] it is known that more than an $H(\kappa^{++})$-strong cardinal is required.

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Sy-David Friedman. Mohammad Golshani. "Killing the $GCH$ everywhere with a single real." J. Symbolic Logic 78 (3) 803 - 823, September 2013. https://doi.org/10.2178/jsl.7803060

Information

Published: September 2013
First available in Project Euclid: 6 January 2014

zbMATH: 1328.03049
MathSciNet: MR3135499
Digital Object Identifier: 10.2178/jsl.7803060

Rights: Copyright © 2013 Association for Symbolic Logic

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Vol.78 • No. 3 • September 2013
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